A successive approximation algorithm for stochastic control problems

Chang, M. H.; Krishna, K. Siva

doi:10.1016/0096-3003(86)90022-6

Cited by 4 publications

(5 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Analytical solutions can be obtained only for some special cases with simple state equations. In this sub section we shall apply the successive approximation algorithm to solve the HJB equation numerically which was introduced in [16]. According to the successive approximation algorithm, the problem of solving the HJB equation numerically has been separated into two sub-problems: (1) Solving the PDE numerically, and (2) Optimization of the nonlinear function over and .…”

Section: A the Iterative Algorithmmentioning

confidence: 99%

“…Then the solution of the optimal submission problem of bid and ask quotes can be obtained by solving the (HamiltonJacobi-Bellman) HJB equation. We employ the successive approximation algorithm introduced by Chang and Krishna [16] to solve the HJB equation which is a second-order partial differential equation (PDE) in coupled with an optimization. The successive approximation algorithm separates the optimization problem from the boundary value PDE problem and thus making the problem solvable by some standard numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal Submission Problem in a Limit Order Book with VaR Constraints

Song¹,

Ching²,

Siu

et al. 2012

2012 Fifth International Joint Conference on Computational Sciences and Optimization

View full text Add to dashboard Cite

We consider an optimal selection problem for bid and ask quotes subject to a value-at-Risk (VaR) constraint when arrivals of the buy and sell orders are governed by a Poisson process. The problem is formulated as a constrained utility maximization problem over a finite time horizon. Using a diffusion approximation to Poisson arrivals of market orders, the dynamic programming principle can be applied here. We propose an efficient procedure to solve this constrained utility maximization problem based on a successive approximation algorithm. Numerical examples with and without the VaR constraint are used to illustrate the effect of the risk constraint on the dealer's choices. We also conduct numerical experiments to analyze the impacts of the risk constraint on dealer's terminal profit.

show abstract

Section: A the Iterative Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Submission Problem in a Limit Order Book with VaR Constraints

Song¹,

Ching²,

Siu

et al. 2012

2012 Fifth International Joint Conference on Computational Sciences and Optimization

View full text Add to dashboard Cite

show abstract

“…As previously mentioned, a necessary condition for an optimal solution of a stochastic control problem is the HJB second-order nonlinear partial differential equation. Analytical solutions of the HJB-PDE can be obtained for some special cases with simple state equations, but more generally we can apply a successive approximation algorithm for a numerical solution via two subproblems [2]:…”

Section: The Successive Approximation Algorithmmentioning

confidence: 99%

“…In Section 2, we describe the cash management problem and derive the Hamilton-Jacobi-Bellman (HJB) second-order nonlinear partial differential equation governing the value function of the optimization problem. The successive approximation algorithm introduced by Chang & Krishna [2] we employ to solve the HJB equation is discussed in Section 3, where our main results and some sensitivity analyses are also presented. Brief Concluding Remarks are made in Section 4.…”

Section: Introductionmentioning

confidence: 99%

On Optimal Cash Management under a Stochastic Volatility Model

Song

Ching

Siu

et al. 2013

E Asian J Appl Math

View full text Add to dashboard Cite

We discuss a mathematical model for optimal cash management. A firm wishes to manage cash to meet demands for daily operations, and to maximize terminal wealth via bank deposits and stock investments that pay dividends and have uncertain capital gains. A Stochastic Volatility (SV) model is adopted for the capital gains rate of a stock, providing a more realistic way to describe its price dynamics. The cash management problem is formulated as a stochastic optimal control problem, and solved numerically using dynamic programming. We analyze the implications of the heteroscedasticity described by the SV model for evaluating risk, by comparing the terminal wealth arising from the SV model to that obtained from a Constant Volatility (CV) model.

show abstract

“…see Grandell [4], where as in Song et al [16] the dynamic programming principle is used to derive an Hamilton-Jacobi-Bellman (HJB) equation. The solution of the optimal submission problem of bid and ask quotes can then be obtained by solving the HJB equation; and we employ the successive approximation algorithm introduced by Chang & Krishna [2] to solve this second-order partial differential equation (PDE), coupled with an optimisation problem. The successive approximation algorithm separates the optimisation problem from the boundary value PDE problem, making the problem solvable by some standard numerical techniques.…”

Section: Introductionmentioning

confidence: 99%

Optimal Strategy for Limit Order Book Submissions in High Frequency Trading

Song

Xie

Ching

et al. 2016

East Asian J. Appl. Math.

View full text Add to dashboard Cite

An optimal selection problem for bid and ask quotes subject to a stock inventory constraint is investigated, formulated as a constrained utility maximisation problem over a finite time horizon. The arrivals of buy and sell orders are governed by Poisson processes, and a diffusion approximation is employed on assuming the Poisson arrivals intensity is sufficiently large. Using the dynamic programming principle, we adopt an efficient numerical procedure to solve this constrained utility maximisation problem based on a successive approximation algorithm, and conduct numerical experiments to analyse the impacts of the inventory constraint on a dealer's terminal profit and stock inventory level. It is found that the stock inventory constraint significantly affects the terminal stock inventory level.

show abstract

A successive approximation algorithm for stochastic control problems

Cited by 4 publications

References 3 publications

Optimal Submission Problem in a Limit Order Book with VaR Constraints

Optimal Submission Problem in a Limit Order Book with VaR Constraints

On Optimal Cash Management under a Stochastic Volatility Model

Optimal Strategy for Limit Order Book Submissions in High Frequency Trading

Contact Info

Product

Resources

About